Question

When a convex lens of focal length 10 cm is placed in contact with a concave lens, the combination has a power of $+5$ diopter. The power of combination, when the lenses are separated by $10$ cm in air, will be

• A. $+10D$
• B. $+20D$
• C. $-5D$
• D. $-30D$

Answer 1

The correct option is A $+10D$

We know, $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$ where f is the focal length of the combination and $f_1$ and $f_2$ are the respective focal lengths of the two lenses.

Where, $f=\frac{1}{5}m=20cm$

$\therefore \frac{1}{20}=\frac{1}{10}+\frac{1}{f_2}$

$\Rightarrow f_2=-20cm$

When lenses are separated, then
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$, where d is the distance between two lenses.

$=\frac{1}{10}-\frac{1}{20}-\frac{10}{10\times (-20)}$

$\Rightarrow f=10cm=0.1cm$

$\therefore p=10diopter$